Class Notes: Finding a Fraction of a Whole Number

Objective

Learn how to calculate a fraction of a whole number by multiplication.

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Key Concepts

• Finding a fraction of a whole number means multiplying the fraction by the whole number.
• Whole numbers can be written as fractions over 1 for easy multiplication.
• You can simplify calculations by canceling common factors before multiplying.

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Examples

Example 1: What is ( \frac{3}{4} ) of 8?

1. Write 8 as a fraction: ( 8 = \frac{8}{1} ).
2. Multiply across:
   • Numerator: ( 3 \times 8 = 24 )
   • Denominator: ( 4 \times 1 = 4 )
3. Simplify: ( \frac{24}{4} = 6 )
4. Answer: 6

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Example 2: What is ( \frac{3}{5} ) of 20?

1. Write 20 as a fraction: ( 20 = \frac{20}{1} ).
2. Multiply across:
   • Numerator: ( 3 \times 20 = 60 )
   • Denominator: ( 5 \times 1 = 5 )
3. Simplify: ( \frac{60}{5} = 12 )
4. Answer: 12

Alternative Simplification

• Express 20 as ( 5 \times 4 ).
• Cancel the 5 in numerator and denominator.
• Multiply: ( 3 \times 4 = 12 ).

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Practice Problems

Try solving these:

1. ( \frac{2}{3} ) of 12
2. ( \frac{5}{7} ) of 28

Solutions

Problem 1: ( \frac{2}{3} ) of 12

• Write as ( \frac{2}{3} \times \frac{12}{1} ).
• 12 can be written as ( 3 \times 4 ); cancel the 3.
• ( 2 \times 4 = 8 ).
• Answer: 8

Problem 2: ( \frac{5}{7} ) of 28

• Write as ( \frac{5}{7} \times \frac{28}{1} ).
• 28 can be written as ( 7 \times 4 ); cancel the 7.
• ( 5 \times 4 = 20 ).
• Answer: 20

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Summary

• Multiply the fraction by the whole number (as a fraction over 1).
• Use cancellation to simplify calculations when possible.
• This method helps to quickly find a fraction of any whole number.